Velocity of Sound in Relaxing Gases

Abstract

ACCURATE measurements of the velocity of sound in a gas, combined with a good equation of state, can yield precise values for the specific heats of the gas. Standing-wave velocity measurements in a tube are complicated by the Helmholtz-Kirchhoff effect which leads to attenuation and a lowered velocity, and by thermal relaxation which causes further attenuation but increase in velocity. It has been shown theoretically¹ that at low audible frequencies the attenuations add linearly while the velocity is the relaxation velocity multiplied by the usual Helmholtz-Kirchhoff factor², that is: where α is the total attenuation, v the measured velocity, f the frequency of oscillation, and α_HK = gf ^½, and α_r = Hτf ² where g is a function of tube radius, viscosity and thermal conductivity, H a function of the principal specific heats and τ the relaxation time. At frequencies such that 2πfτ ≪ 1, the relaxation velocity v _r reduces to the free space velocity at zero frequency v ₀. Using the apparatus described by Harlow³, measurements were made on pure carbon dioxide, pure oxygen and dry air free from carbon dioxide of the velocity of sound and corresponding attenuation at frequencies between 100 and 1,500 cycles sec.⁻¹, at a pressure of one atmosphere and temperature of 30° C. By plotting v ⁻¹ against f^−½ straight line graphs were obtained and the values of v ₀ and g determined. Graphs of αf ^−½ against f ^3/2 yielded values for g and Hτ. These values are given in Table 1 together with the theoretical values of g and H and the value of τ in the samples used.